A209168 Triangle of coefficients of polynomials u(n,x) jointly generated with A209169; see the Formula section.

1, 2, 1, 4, 6, 3, 7, 16, 17, 7, 12, 37, 56, 47, 17, 20, 78, 154, 182, 128, 41, 33, 156, 378, 574, 565, 344, 99, 54, 301, 864, 1590, 1995, 1697, 915, 239, 88, 566, 1877, 4048, 6118, 6605, 4973, 2413, 577, 143, 1044, 3927, 9693, 17073, 22128, 21093

Offset

1,2

Comments

Row n begins with F(n+2)-1, where F=A000045 (Fibonacci numbers).

Alternating row sums: 1,1,1,1,1,1,1,1,1,1,1,1,1,1,...

For a discussion and guide to related arrays, see A208510.

Links

Table of n, a(n) for n=1..52.

Formula

u(n,x)=u(n-1,x)+(x+1)*v(n-1,x),

v(n,x)=(x+1)*u(n-1,x)+2x*v(n-1,x)+1,

where u(1,x)=1, v(1,x)=1.

Example

First five rows:
1
2....1
4....6....3
7....16...17...7
12...37...56...47...17
First three polynomials v(n,x): 1, 2 + x, 4 + 6x + 3x^2.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x];
v[n_, x_] := (x + 1)*u[n - 1, x] + 2 x*v[n - 1, x] + 1;
Table[Expand[u[n, x]], {n, 1, z/2}]
Table[Expand[v[n, x]], {n, 1, z/2}]
cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
TableForm[cu]
Flatten[%]    (* A209168 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A209169 *)

Crossrefs

Cf. A209169, A208510.

Sequence in context: A105364 A180405 A171007 * A209162 A127366 A064786

Adjacent sequences: A209165 A209166 A209167 * A209169 A209170 A209171

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 08 2012

Status

approved